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A242104 Sum s of consecutive digits of Pi such that s is prime. 0
3, 5, 17, 11, 3, 5, 17, 7, 17, 47, 2, 7, 37, 17, 67, 29, 13, 11, 3, 7, 19, 89, 97, 19, 23, 43, 5, 5, 5, 23, 2, 5, 3, 5, 13, 11, 23, 7, 11, 13, 2, 7, 13, 13, 2, 2, 5, 5, 5, 19, 23, 53, 43, 47, 3, 3, 17, 19, 5, 23, 3, 7, 29, 3, 7, 5, 2, 7, 3, 19, 5, 5, 23, 23, 3, 13, 19, 13, 3, 2, 89, 7, 3, 7, 2, 17, 7, 131, 2, 5, 13, 17, 13, 13, 17, 2, 5, 19, 7, 5, 3, 5, 43, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A histogram of the first 1.4 million terms in this sequence reveals 7 as the most common term with a frequency of 15.25%.  The smaller primes (2,3, and 5) occur with frequencies between 12% and 14%, and larger primes rapidly decrease in frequency.  99% of the terms are composed of the first 20 primes (2,3,5,...,71).  The largest of the first 1.4 million terms is a(220693)=281, which is the sum of an otherwise prime-free sum of 64 consecutive digits of Pi (6+9+3+9+5+4+6+9+7+5+5+9+9+6+4+0+0+8+2+9+7+6+0+0+5+3+5+4+1+8+8+6+6+1+7+8+8+2+3+1+1+1+0+2+0+1+7+2+7+1+5+5+7+3+0+2+2+5+5+0+5+9+5+2).

LINKS

Table of n, a(n) for n=1..104.

EXAMPLE

a(1)=3 because it is the first digit of Pi, and it is prime.

a(2)=1+4=5 because it is the sum of the next consecutive digits of Pi, and it is prime, and the prior sum (1) is not prime.

a(3)=1+5+9+2=17 because it is the sum of the next consecutive digits of Pi, and it is prime, and prior sums (1,1+5=6,1+5+9=15) are not prime.

CROSSREFS

Cf. A000040, A000796.

Sequence in context: A192911 A105408 A291963 * A158895 A085418 A292008

Adjacent sequences:  A242101 A242102 A242103 * A242105 A242106 A242107

KEYWORD

nonn,base

AUTHOR

Gil Broussard, Aug 15 2014

STATUS

approved

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Last modified December 10 20:23 EST 2019. Contains 329909 sequences. (Running on oeis4.)